Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-4y &= -1 \\ -7x-8y &= -5\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-7x = 8y-5$ Divide both sides by $-7$ to isolate $x$ $x = {-\dfrac{8}{7}y + \dfrac{5}{7}}$ Substitute this expression for $x$ in the first equation. $-({-\dfrac{8}{7}y + \dfrac{5}{7}}) - 4y = -1$ $\dfrac{8}{7}y - \dfrac{5}{7} - 4y = -1$ Simplify by combining terms, then solve for $y$ $-\dfrac{20}{7}y - \dfrac{5}{7} = -1$ $-\dfrac{20}{7}y = -\dfrac{2}{7}$ $y = \dfrac{1}{10}$ Substitute $\dfrac{1}{10}$ for $y$ in the top equation. $-x-4( \dfrac{1}{10}) = -1$ $-x-\dfrac{2}{5} = -1$ $-x = -\dfrac{3}{5}$ $x = \dfrac{3}{5}$ The solution is $\enspace x = \dfrac{3}{5}, \enspace y = \dfrac{1}{10}$.